Search results for "MATHEMATICS"
showing 10 items of 22031 documents
Teaching programming by emphasizing self-direction: How did students react to the active role required of them?
2013
Lecturing is known to be a controversial form of teaching. With massed classrooms, in particular, it tends to constrain the active participation of students. One of the remedies applied to programming education is to use technology that can vitalize interaction in the classroom, while another is to base teaching increasingly on programming activities. In this article, we present the first results of an exploratory study, in which we teach programming without lectures, exams, or grades, by heavily emphasizing programming activity, and, in a pedagogical sense, student self-direction. This article investigates how students reacted to the active role required of them and what issues emerged in …
A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne-Weinberger inequality
2015
We consider evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and exact solution of the problem. The estimates (majorants and minorants) are explicitly computable and do not contain unknown functions or constants. Moreover, it is proved that the estimates are equivalent to the energy norm of the deviation from the exact solution.
Open Resources as the Educational Basis for a Bachelor-level Project-Based Course
2015
This article presents an innovation-based course concept for project-based learning. In this course, student groups are asked to ideate and implement a software product based on Open Data and Open API releases. By emphasizing studentsâ own product ideation, the course requires and enhances self-directed learning skills and prompts the students to see the unlimited possibilities in becoming and being a practitioner of the computing discipline. Relatedly, the course provides a tool to improve student self-efficacy, as the students, coached through challenges, come to know that they are able to produce software using various open interfaces.
Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models
2017
Abstract European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like the Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a give…
Interactive Multiple Criteria Decision Making based on preference driven Evolutionary Multiobjective Optimization with controllable accuracy
2012
Abstract We present an approach to interactive Multiple Criteria Decision Making based on preference driven Evolutionary Multiobjective Optimization with controllable accuracy. The approach relies on formulae for lower and upper bounds on coordinates of the outcome of an arbitrary efficient variant corresponding to preference information expressed by the Decision Maker. In contrast to earlier works on that subject, here lower and upper bounds can be calculated and their accuracy controlled entirely within evolutionary computation framework. This is made possible by exploration of not only the region of feasible variants – a standard within evolutionary optimization, but also the region of i…
Reduced Order Models for Pricing American Options under Stochastic Volatility and Jump-diffusion Models
2016
American options can be priced by solving linear complementary problems (LCPs) with parabolic partial(-integro) differential operators under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. These operators are discretized using finite difference methods leading to a so-called full order model (FOM). Here reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD) and non negative matrix factorization (NNMF) in order to make pricing much faster within a given model parameter variation range. The numerical experiments demonstrate orders of magnitude faster pricing with ROMs. peerReviewed
Iterative Methods for Pricing American Options under the Bates Model
2013
We consider the numerical pricing of American options under the Bates model which adds log-normally distributed jumps for the asset value to the Heston stochastic volatility model. A linear complementarity problem (LCP) is formulated where partial derivatives are discretized using finite differences and the integral resulting from the jumps is evaluated using simple quadrature. A rapidly converging fixed point iteration is described for the LCP, where each iterate requires the solution of an LCP. These are easily solved using a projected algebraic multigrid (PAMG) method. The numerical experiments demonstrate the efficiency of the proposed approach. Furthermore, they show that the PAMG meth…
Synchronous R-NSGA-II: An Extended Preference-Based Evolutionary Algorithm for Multi-Objective Optimization
2015
Classical evolutionary multi-objective optimization algorithms aim at finding an approx- imation of the entire set of Pareto optimal solutions. By considering the preferences of a decision maker within evolutionary multi-objective optimization algorithms, it is possible to focus the search only on those parts of the Pareto front that satisfy his/her preferences. In this paper, an extended preference-based evolutionary algorithm has been proposed for solving multi-objective optimiza- tion problems. Here, concepts from an interactive synchronous NIMBUS method are borrowed and combined with the R-NSGA-II algorithm. The proposed synchronous R-NSGA-II algorithm uses preference information provid…
A New Augmented Lagrangian Approach for $L^1$-mean Curvature Image Denoising
2015
Variational methods are commonly used to solve noise removal problems. In this paper, we present an augmented Lagrangian-based approach that uses a discrete form of the L1-norm of the mean curvature of the graph of the image as a regularizer, discretization being achieved via a finite element method. When a particular alternating direction method of multipliers is applied to the solution of the resulting saddle-point problem, this solution reduces to an iterative sequential solution of four subproblems. These subproblems are solved using Newton’s method, the conjugate gradient method, and a partial solution variant of the cyclic reduction method. The approach considered here differs from ex…
Mobile Banking Services Continuous Usage -- Case Study of Finland
2016
Finland is at the forefront of using new information systems, such as mobile banking (m-banking). The present study develops and tests a model of continuous usage intentions toward m-banking services for a sample of 273 Finnish m-banking users. Results confirm the hypothesized direct relationships between self-congruence and perceived value, perceived risk and perceived value, perceived value and continuous usage, and continuous usage and word of mouth. The frequency of usage of m-banking services and experience moderate the relationship between perceived value and continuous usage. We discuss the theoretical and managerial implications of the study results and present recommendations for f…